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A dominating set D in a graph is a subset of its vertex set such that each vertex is either in D or has a neighbour in D. In this paper, we are interested in an output-sensitive enumeration algorithm of (inclusionwise) minimal dominating sets in graphs, called Dom problem. It was known that this problem can be polynomially reduced to the well known… (More)

In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split… (More)

We reduce (in polynomial time) the enumeration of minimal dominating sets in interval and permutation graphs to the enumeration of paths in DAGs. As a consequence, we can enumerate in linear delay, after a polynomial time pre-processing, minimal dominating sets in interval and permutation graphs. We can also count them in polynomial time. This improves… (More)

A hypergraph is a pair pV, Eq where V is a finite set and E Ď 2 V is called the set of hyper-edges. An output-polynomial algorithm for C Ď 2 V is an algorithm that lists without repetitions all the elements of C in time polynomial in the sum of the size of H and the accumulated size of all the elements in C. Whether there exists an output-polynomial… (More)

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transver-sal problem which asks for an output-polynomial algorithm for listing the set of minimal hitting sets in hypergraphs. We give a polynomial delay algorithm to list the set of minimal… (More)

In this paper we address the problem of generating all elements obtained by the saturation of an initial set by some operations. More precisely, we prove that we can generate the closure by polymorphisms of a boolean relation with a polynomial delay. Therefore we can compute with polynomial delay the closure of a family of sets by any set of " set… (More)

Synthetic biology has boomed since the early 2000s when it started being shown that it was possible to efficiently synthetize compounds of interest in a much more rapid and effective way by using other organisms than those naturally producing them. However, to thus engineer a single organism, often a microbe, to optimise one or a collection of metabolic… (More)